nLab Langlands analogies -- table

analogies in the Langlands program:

arithmetic Langlands correspondence	geometric Langlands correspondence
ring of integers of global field	structure sheaf on complex curve $\Sigma$
Galois group	fundamental group of $\Sigma$
Galois representation	flat connection/local system on $\Sigma$
idele class group mod integral adeles	moduli stack of line bundles on $\Sigma$
nonabelian $\;$ “	moduli stack of vector bundles on $\Sigma$
automorphic representation	Hitchin connection D-module on bundle of conformal blocks over the moduli stack